Customized z-lens design program

ABSTRACT

Embodiments of the invention pertain to a method for producing a spectacle lens with optimal correction across the entire lens taking into account the patient&#39;s complete measured wavefront. Specific embodiments can also take into account one or more additional factors such as vertex distance, SEG height, pantoscopic tilt, and use conditions. The lens wavefront can be achieved by optimizing a corrected wavefront, where the corrected wavefront is the combined effect of the patient&#39;s measured wavefront and the lens wavefront. The optimization of the corrected wavefront can involve representing the measured wavefront and the lens wavefront on a grid. In an embodiment, the grid can lie in a plane. During the optimization, a subset of the grid can be used for the representation of the measured wavefront at a point on the grid so as to take into account the portions of the measured wavefront that contribute to the corrected wavefront at that point on the grid.

BACKGROUND OF INVENTION

Ocular lenses are worn by many people to correct vision problems. Visionproblems are caused by aberrations of the light rays entering the eyes.These include low order aberrations, such as myopia, hyperopia, andastigmatism, and higher order aberrations, such as spherical, coma,trefoil, and chromatic aberrations. Because the distortion introduced byaberrations into an optical system significantly degrades the quality ofthe images on the image plane of such system, there are advantages tothe reduction of those aberrations.

Ocular lenses are typically made by writing prescriptions to lensblanks. This is accomplished by altering the topography of the surfaceof a lens blank.

Recently, attention has been given to methods of writing a low orderlens using a patient's measured wavefront information. Currently,several techniques can be utilized to determine the optimum low orderrefraction from the high order, including: the Gaussian Least SquaresFit, point spread optimization, and neural network analysis. Some ofthese techniques may be employed to not only derive the best low orderprescription from the high order values, but may also be used to “fit”an optimum wavefront across an entire spectacle lens based on thepatient's measured wavefront.

Using one or more of these fitting techniques may yield a betterrefraction than conventional subjective refractions in the center zone,but consideration must be given to off-axis gaze angles. In particular,one considerable disadvantage of traditional lens manufacturing is thatthat many people experience distortion when looking off-center outsidethe central region, commonly called “swim”.

Accordingly, there is a need for a method of determining a wavefront fora patient's spectacle based on the patient's measured wavefront, in sucha way to reduce distortion when the patient looks off center outside thecentral region.

BRIEF SUMMARY

The subject invention provides methods for determining a wavefront for alens from a patient's measured wavefront. The wavefront can be used forproducing a spectacle lens with optimal correction across the entirelens taking into account the patient's complete measured wavefront.Specific embodiments can also take into account one or more additionalfactors such as vertex distance, SEG height, pantoscopic tilt, and useconditions.

The lens wavefront can be achieved by optimizing a corrected wavefront,where the corrected wavefront is the combined effect of the patient'smeasured wavefront and the lens wavefront. In one embodiment of thesubject invention, the optimization of the corrected wavefront involvesrepresenting the measured wavefront and the lens wavefront on a grid. Inan embodiment, the grid can lie in a plane. During the optimization, asubset of the grid can be used for the representation of the measuredwavefront at a point on the grid so as to take into account the portionsof the measured wavefront that contribute to the corrected wavefront atthat point on the grid.

BRIEF DESCRIPTION OF FIGURES

FIG. 1 shows the steps for a method for producing a spectacle lens inaccordance with an embodiment of the subject invention.

FIG. 2 shows a flow chart in accordance with an embodiment of thesubject invention.

FIG. 3 shows a top view of spectacle and pupil samples as images atparticular shift (gaze).

FIG. 4 shows a side view of spectacle and eye, on the left withcorresponding dotted lines, with gaze rotation shown by the curved arrowand the rotated eye and corresponding dotted lines the curved arrow ispointing to and gaze shift shown by the straight arrow and the shiftedeye and corresponding dotted lines the straight arrow is pointing to onthe right.

FIG. 5 shows a schematic representation of an approximation ofrepresenting the i-th direction as the i-th shift.

FIG. 6 shows a comparison of off-axis versus transverse correction forspectacle lens applications.

FIG. 7 shows a schematic representation of a transverse correction for acontact lens application.

FIG. 8 shows a schematic representation of a lens blank with a monofocalhigher-order region and a transition zone.

FIG. 9 shows a lens image.

FIGS. 10A-10D show an example of trefoil.

FIGS. 11A-11D show an example of coma.

FIGS. 12A-12D show an example of spherical aberration.

DETAILED DESCRIPTION

The subject invention provides methods for determining a wavefront for alens from a patient's measured wavefront. The wavefront can be used forproducing a spectacle lens with optimal correction across the entirelens taking into account the patient's complete measured wavefront.Specific embodiments can also take into account one or more additionalfactors such as vertex distance, SEG height, pantoscopic tilt, and useconditions.

The lens wavefront can be achieved by optimizing a corrected wavefront,where the corrected wavefront is the combined effect of the patient'smeasured wavefront and the lens wavefront. The optimization of thecorrected wavefront can involve representing the measured wavefront andthe lens wavefront on a grid. In one embodiment, the grid can lie in aplane. During the optimization, a subset of the grid can be used for therepresentation of the measured wavefront at a point on the grid so as totake into account the portions of the measured wavefront that contributeto the corrected wavefront at that point on the grid.

One embodiment of the invention utilizes the hill climbing optimizationtechnique used in the Gaussian Least Squares Fit and point spreadoptimization software to fit an optimal wavefront across a specifiedsurface larger than that of the measured wavefront. The desiredwavefront is projected from a number of points emanating in multipledirections from a nominal axis of rotation representing the center ofthe eye. The wavefront pattern used can be solely based upon the loworder, or can also include some or all the high order as well.

Each position of the wavefront as projected from the center of the eyecan be convolved with a weighting function across the lens to enhance oremphasize the wavefront in certain areas while allowing other areas tobe de-emphasized. The wavefront is best fit along a surface representinga paraxial lens representing the neutral axis of a lens. This paraxiallens is fixed in space at a specified central vertex distance andfollows the basic lens design curvature of the chosen blank lens. Thebasic lens design curvature may be simply derived from the centrallower-order prescription or may be used in conjunction with the highorder and other factors such as vertex distance.

The final wavefront can be fitted with one or more of the followinginputs:

Wavefront

Pupilary Distance

Vertex Distance

Pantoscopic Tilt

SEG Height

Pupil Diameter

Conditions under which the lens will be used (day, office, night, etc)

Age

OD Subjective refraction

ADD Value

Spectacle Geometry

FIG. 1 shows the steps for one embodiment of a method for producing aspectacle lens in accordance with the subject invention and FIG. 2 showsa flowchart indicating the flow of information in accordance with anembodiment of a wavefront optimization method. In one embodiment, vertexdistance and its effect on the lens power and astigmatism can becompensated for in the wavefront fitting process. The output of thewavefront fitting software process (steps 1 & 2 in FIG. 1) is a set ofinstructions that facilitates production of a custom lens.

Various techniques may be utilized to generate the actual lens. Forexample; the instructions may include a surface map for front and/orback surfaces of a lens, or a points file that can be fed into afreeform lens generator, to cut custom front and back surfaces. Otherapproaches may utilize a changeable refractive index layer within thelens blank that can be customized with the information from the fittingsoftware. Yet another approach can use an inkjet deposition of differentrefractive indices across a lens surface to generate a correctedwavefront based on the fitting software output. In yet another approach,stereo lithography may he used in conjunction with casting, orcombination of any of the above techniques can be combined to achievethe custom lens manufacturing.

Step 3 in FIG. 1 represents a freeform grinding approach to lensmanufacturing. Casting, inkjet, and sandwiched changeable refractiveindex approaches as known in the art, can also be utilized.

If utilizing the freeform grinding approach the final step in thewavefront fitting software can generate shape of the front and backsurface of the lens to achieve the given wavefront. Development of theshape of the front and back surface can also take into account thedistortions from lens thickness variations to minimize distortions. Theoutput of the fitted wavefront software can, in an embodiment, be apoints file, which can subsequently be transferred into a freeform lensgenerator for manufacturing the lens. The resulting lens can beessentially optimized across the entire lens and customized for eachpatient based on all the input parameters. This freeform grindingtechnique can be utilized in conjunction with the refractive indexchanging material to further tune or enhance the refractive propertiesafter lens grinding and polishing.

In one embodiment, a grid of shifts (rather than rotations) for measuredand target pupil wavefronts is used, represented mathematically byimages. The target wavefront can be used as the lens wavefront. From themeasured wavefront, the target wavefront can be determined via one ormore embodiments of the invention. A variety of configurations can beused to implement the target wavefront via an eyeglass for the patient.

As an example, a single lens with two surfaces can be used to create aneyeglass for a patient, where one or both of the lens surfaces can becontrolled to effect the wavefront for the lens. Alternatively, two lensblanks each having two surfaces can be used with a variable indexpolymeric material between the two lens blanks, where one or more of thefour lens blank surfaces and/or the polymeric material can be controlledto effect the wavefront for the lens. The lens surface(s) and/orvariable cured index of the polymeric material of the polymeric materialare described in a two-dimensional plane corresponding to the height ofthe surface(s) or the projection of the index layer(s) onto a plane.

Aberrations are measured as components in an orthogonal expansion of thepupil sampled on the same grid spacing. In a specific embodiment, thegrid spacing is about 0.5 mm and in another embodiment the grid spacingis about 0.1 mm. In an embodiment using Zernike polynomials, thecomponents can be made orthogonal for the chosen pupil size due todiscrete sampling. As an example, the components can be made orthogonalthrough a process such as Gram-Schmidt orthogonalization. Orthogonalcomponents of aberrations for pupils centered at a specific point on thespectacle may then be computed by sample-by-sample multiplication (innerproduct) of the aberration component image with the lens (height orprojection) image centered at the point of interest, as in FIG. 3. FIG.3 shows a top view of spectacle and pupil samples as images atparticular shift (gaze), which can be used for computation ofaberrations for pupils having a diameter of 3 samples, centered at achosen coordinate on a spectacle grid having a diameter of 8 samples.

Zernike polynomials are orthogonal and when samples are taken,approximations of Zernike polynomials can be created. In one embodiment,the approximations of Zernike polynomials can then be modified to makeorthogonal polynomials, so as to create new polynomials.

In an embodiment, points on the pupil outside the pupil diameter areassumed zero. Non-squared pupil shapes may be formed by zeroing selectpoints within the square of pupil diameter. Mathematically, the processof computing the inner product centered at all possible locations on thegrid is a cross correlation, which may be implemented with a fastconvolution algorithm. An image can be produced for each Zernike via thecross-correlation. The image for each Zernike can be used to create atarget and an error. The error can be used to produce an errordiscrimination, or a weighted sum of all pixels in the image square.

In a specific embodiment, a grid size and spacing is chosen to representthe lens and pupil in a plane. An example of such a grid is shown inFIG. 3. The aberrations of interest are orthogonalized on the grid atthe chosen pupil size. Then a given aberration centered at every pointmay be estimated by cross-correlation of the orthogonalized Zernikeimage and the spectacle image, resulting in an image for each Zernikecomponent. An error image for each point on the lens may be estimated asa difference between the computed and desired Zernike aberrationcentered at each point in the image.

The desired correction is, to a first approximation, assumed to beconstant in this plane with a shift corresponding to a given gaze angle.The rotation is otherwise neglected as shown in FIG. 2. For large gazeangles, the effect of rotation can be compensated by providing aspatially-varying correction target. The spatially-varying target can beapproximated by rotating the paraxial target.

Simple convolution may be replaced with a more exact geometriccalculation of the ray-surface intersection corresponding to aray-tracing-style algorithm over a fixed grid. Other grid geometries maybe used (e.g., hexagonal instead of rectangular). The result isessentially a spatially varying sample spacing and convolution,increasing computation time.

Other metrics of surface error may be computed from the Zernikecomponent error images, as done with single pupil representations.Images of sphere/cylinder/values (or errors from desired) may becomputed by applying the usual conversion on a pixel-by-pixel basis forexample.

Total root-mean-square (rms) may be represented by either the sum of allcomponent terms squared for a particular pupil location, or the sum ofall pixels squared (and properly normalized) within the pupil. This maybe achieved by cross-correlations of a pupil-sized aperture of ones withan image of the lens values squared. Total high order may be computed bysubtracting the low order aberration images from the total rms image.High order error may be computed by also subtracting the target highorder images, squared pixel-by-pixel. For certain error choicesoptimizing error this may be mathematically equivalent to knownregularization algorithms.

A total error discriminant may be generated by summing desired errorimages over the entire lens. A pixel-by-pixel weighting may beincorporated to selectively weight the error at various regions in thelens, and this may be done independently for each Zernike component.Standard optimization procedures (e.g., convex programming) may be usedto produce a lens image that minimizes the error discriminant. If thelens image is sufficiently small, the cross-correlation may berepresented as a matrix multiplication further simplifying theapplication of optimization algorithms known in the art. For largerimage sizes this may be impractical, but may still be used to adapt thealgorithm to the problem before implementing with fast convolutionalgorithms.

Constraints on the error may also be used in the optimization that wouldbe represented by constraint images of max and/or min Zernike componentsor functions thereof. An example of a constraint that can be utilized isthat the error for a certain Zernike cannot be above a certain thresholdfor a certain area.

Free-floating points, such as boundaries, may be handled by settingweights to zero or very small for those points. This allows theoptimized region to be smaller than the actual grid, the optimizedregion to have an arbitrary shape, and/or the optimized region to onlybe optimized for points that will ultimately be used. In a specificembodiment, the patient-selected frame outline may be input as theregion of optimization. As there can be an infinite number of solutions,an attempt can be made to optimize a certain shape inside of the lenses,such as the spectacle shape. An example of a certain shape that can beoptimized is to optimize within the shape of the frame that the lenswill be used by, for example, using a zero weight outside of the frame.

Fixed points, which are given prior to optimization and remainunchanged, may be provided by using the points to compute correction butnot applying it to them in the optimization algorithm. This can be usedfor boundaries, so as to only optimize for certain portions of lenses.

Grid(s) of constraints may be converted into a weighting and/or target(for unconstrained optimization) via a separate optimization procedure.

Multiple surfaces may be optimized simultaneously. As an example, twogrids can be optimized simultaneously or each grid point can have twonumbers associated with it to be optimized.

The patient's prescription (including high order) may be used as target,including deterministic variations with gaze if available.

Example 1 Simple Alignment Tolerant Lens

For purposes of this example, lower case bold letters denote matrices(or equivalently, images), which describe either the two-dimensional(single-surface) lens as a optical-path delay (OPD) map, or atwo-dimensional wavefront, also as an OPD map.

-   a_(i,j) Corrected wavefront aberration in the (i,j)^(th) position.-   i, j Indices i^(th) horizontal and j^(th) vertical positions.-   n, m Indices of matrix elements.-   L Total number of pixels on side of (square) pupil and aberration    matrices.-   N Total number of pixels on side of (square) spectacle OPD matrix.-   p, Pupil aberration OPD,-   p_(i,j) pupil aberration in the (i,j)^(th) position if it changes    with gaze.-   s Spectacle OPD over entire range of lens, e.g. 50 mm diameter-   g Matrix describing weighting of error over pupil-   z_(k) k-th (sampled) Zernike wavefront matrix-   w(i,j), Weighting over angle,-   w_(k)(i,j) Weighting over angle for the k^(th) Zernike term-   f Objective function

An assumption can be made that an optimization of image quality for alens over a range of gaze angles can be well approximated by anoptimization of image quality over a range of translations. The rotationof the eye relative to the lens is, therefore, ignored in this example.The desired OPD calculated through optimization can be converted to, forexample, a surface or pair of surfaces via a ray-tracing application.

The corrected wavefront aberration in the (i,j)^(th) position, includingboth the pupil aberation p and the corresponding apertured portion ofthe spectacle s, is described as

$\begin{matrix}{{{{a_{i,j}\left( {n,m} \right)} = {{p\left( {n,m} \right)} + {s\left( {{n + i},{m + j}} \right)}}};n},{m = {- \frac{L}{2}}},\ldots \mspace{14mu},\frac{L}{2}} & (1)\end{matrix}$

a, p, and s are matrices. The total error to be optimized will be afunction of all the a_(i,j). The matrices can have zeroes as entries forinput data or output data that is, for example, circular, rectangular,or has a non-square pattern. The simplest function is the total squarederror over all shifts with weightings over both the shifts and thepupil, which can be represented as shown in Equation (2).

$\begin{matrix}{f = {\sum\limits_{i,j}{{w\left( {i,j} \right)}{\sum\limits_{n,m}{{g\left( {n,m} \right)}\left\lbrack {a_{i,j}\left( {n,m} \right)} \right\rbrack}^{2}}}}} & (2)\end{matrix}$

One approach to optimize the corrected wavefront is to preferentiallyselect certain Zernike terms to be corrected or excluded. An example ofpreferential selection of certain Zernike terms is to only correctastigmatism for a Progressive-Addition Lens (PAL) design. To select thecomponent of the chosen Zernike term(s) from the full wavefrontaberration we make use of the orthonomality of Zernikes and simply takethe inner product of each Zernike with the wavefront in Equation (1).

$\begin{matrix}\begin{matrix}{{a_{i,j}\left( {n,m} \right)} = {{z_{0}{\sum\limits_{n,m}\left\{ {{z_{0}\left( {n,m} \right)}{a_{i,j}\left( {n,m} \right)}} \right\}}} +}} \\{{{z_{1}{\sum\limits_{n,m}\left\{ {{z_{1}\left( {n,m} \right)}{a_{i,j}\left( {n,m} \right)}} \right\}}} + \ldots}} \\{= {\sum\limits_{k = 0}^{\infty}{z_{k}{c_{k}\left( {i,j} \right)}}}}\end{matrix} & (3)\end{matrix}$

The coefficient matrix for the k-th Zernike, e_(k)(i, j), can becomputed as

$\begin{matrix}\begin{matrix}{{c_{k}\left( {i,j} \right)} = {\sum\limits_{n,m}\left\{ {{z_{k}\left( {n,m} \right)}{a_{i,j}\left( {n,m} \right)}} \right\}}} \\{= {z_{k}*a_{i,j}}}\end{matrix} & (4)\end{matrix}$

which uses the cross-correlation operation or, equivalently, theconvolution operation implemented appropriately.

Particular Zernike components of the aberration can be selectivelyweighted by weighting the component in (3)

$\begin{matrix}{{a_{i,j}^{\prime}\left( {n,m} \right)} = {\sum\limits_{k = 0}^{\infty}{{w_{k}\left( {i,j} \right)}{c_{k}\left( {i,j} \right)}z_{k}}}} & (5)\end{matrix}$

The appropriate w_(k) may be set to zero to ignore certain components.

The simplest approach, and one of very few that can be solvedanalytically, is to optimize a weighted total squared error over allgaze positions, or shifts, where the error is defined according somecarefully chosen and/or excluded combination of Zernikes.

It is aparrent that the minimum least-squares optimum over anangle-range larger than the pupil diameter with no weighting will resultin a purely low-order solution. However if a weighting is used it ispossible to trade off improvement in some areas for others.

Combining equations (2) and (5), the squared error objective is then

$\begin{matrix}\begin{matrix}{f = {\sum\limits_{i,j}{\sum\limits_{n,m}{{g\left( {n,m} \right)}\left\lbrack {\sum\limits_{k = 0}^{\infty}{{w_{k}\left( {i,j} \right)}{c_{k}\left( {i,j} \right)}z_{k}}} \right\rbrack}^{2}}}} \\{= {\sum\limits_{i,j}{\sum\limits_{n,m}{{g\left( {n,m} \right)}\left\lbrack {\sum\limits_{k = 0}^{\infty}{{w_{k}\left( {i,j} \right)}\left( {z_{k}*\begin{pmatrix}{{p\left( {n,m} \right)} +} \\{s\left( {{n + i},{m + j}} \right)}\end{pmatrix}} \right)z_{k}}} \right\rbrack}^{2}}}}\end{matrix} & (6)\end{matrix}$

which may be solved via standard optimization algorithms for the optimals.

Making the weighting w (n,m) the same for every Zernike term allows ananalytical solution. Setting the gradient of equation (6) with respectto s equal to zero yields an optimized result which can be written asfollows:

s=−{w*(g×p)}/{w*g}  (7)

The “×” and “/” operators indicate element-by-element multiplication ordivision respectively, and the “*” operator indicates two-dimensionalconvolution.

Using a uniform pupil-weighting further simplifies equation (7) to

s=−{w*p}/{w*l}  (8)

Where l is simply a matrix of ones, resulting in a low-pass filtered win the denominator term. So the result is a convolution of the weightingwith the aberration that is normalized by a filtered version of theweighting.

Some simulated examples for certain zernike terms are provided in FIGS.10A-10D, FIGS. 11A-11D, and FIGS. 12A-12D, where FIGS. 10A-10D show anexample of trefoil, FIGS. 11A-11D show an example of coma, and FIGS.12A-12D show an example of spherical aberration. Note that theamplitudes are normalized for a 1 um rms aberration, and the y-axis isnormalized to the zernike diameter. One-dimensional cross-sections ofthe lens, error are provided. Again, FIGS. 10A-10D show the results fortrefoil; FIGS. 11A-11D show the results for coma; and FIGS. 12A-12D showthe results for spherical aberration.

Referring to Example 1, several different methods can be reflected indifferent choices of g, the matrix describing weighting or error overpupil, with q_(ij) being effective pupil aberration for the i, jposition and h being a matrix describing weighting of wavefront overpupil. Examples of several methods are provided in Table 1.

TABLE 1 Mathematical Step Description of Method g = I, the identitymatrix Standard Least Squares g_(w) = diag{g}, diagonal matrix LeastSquares weighted over pupil g = hg_(w)h, h = z₃z₃ ^(T) + z₅z₅ ^(T)Minimum Astigmatism - PAL design g = hg_(w)h, h = I − z₀z₀ ^(T) FreeVarying Piston g = hg_(w)h, Free Varying Tilt - distortion allowed h = I− z₀z₀ ^(T) − z₁z₁ ^(T) − z₂z₂ ^(T) q_(ij) = p_(ij) − i c₁z₁ − i c₂(i)z₂Constantly Changing Tilt - Magnification

Another approach can require an “unknown prescribed Zernike”. This canbe used, for example, to yield a tilt that is constant (as possible)over the lens but not necessarily zero. For certain aberrations this canresult in an improved vision quality by allowing some magnification,which in this treatment can be referred to as linear distortion. Thiscan be achieved by iteratively varying the values for c_(1,desired) andc_(2,desired) with some allowable range and choosing the pair thatresults in the lowest error minimum.

Aberration Bandwidth

An approach at optimizing a metric based on the point-spread function(PSF) can be performed via consideration of the spatial “bandwidth” as ametric of the PSF at a specific gaze angle. If a wavefront can bedescribed as a two-dimensional single-component FM signal, then itslocal spatial frequency content at a given point can be estimated formthe spatial derivatives of the phase. By estimating the average meansquared value of the spatial derivative of the wavefront, an estimate ofthe bandwidth of the PSF can be produced.

An estimate for the averaged bandwidth of the PSF can be described asDa,

where D is a matrix that computes the averaged local derivative viafinite differences. There is a variety of possible choices for D toapproximate a derivative.

An approach similar to the use of a matrix that computes the averagedlocal derivative via finite differences approach of Example 1, but usingderivatives of the pupil and spectacle, can be used.

In another embodiment, D can be selected to approximate a secondderivative, in order to approximate power matching.

Region-Based Optimization

In an embodiment, optimization can be performed using a standarditerative approach such as Gradient Descent with some chosen boundaryconditions. These boundary conditions can describe the required outcomeat the edges of the lens as well as in zones in its interior. A varietyof different applications can be addressed by selecting these regions.

Transition Zones

Transition zone based lens designs have the requirement of perfectionfor the axial ray and for the correction at some outer radius to be aconstant (or low-order). Therefore, the single zone's correction can bepredetermined as some high-order correction, then the optimization canvary only a narrow region outside this zone to find the optimum lens.The remaining region outside this transition zone can be required to besome flat or low-order correction.

Progressive-Addition Lenses

Progressive-Addition Lenses (PAL's) have required low-order correctionin a pair of zones, with some varying power along a line connectingthem. Typically, the rest of the lens is then optimized to reducedistortion. In an embodiment of the subject invention, the lens can beoptimized to similarly reduce distortion. The lens can be optimized toreduced distortion via, for example, power matching, matching secondorder wavefronts only, or full-wavefront matching with a varying tilt.

Example 2 Simple Rotation and Alignment Tolerant Lens Design

This Example uses a method for optimizing the correction “programmed”onto a higher-order contact lens. Contact lenses can be designed to bein a certain orientation, but can still rotate with respect to thisorientation and can slide as well so as to become decentralized. Theunpredictable rotation and decentration of the lens during normalwearing can be addressed. Given a range of rotations and decentrations,the contact lens design is optimized to improve vision throughout theentire range by minimizing the total wavefront error summed over theranges. The optimum over decentrations may be computed as in Equation(7) provided in Example 1. The optimum over rotations is computed asfollows.

The error discriminant is:

$\begin{matrix}{f = {\sum\limits_{\theta}{{w(\theta)}{\sum\limits_{n,m}\left\lbrack {{p\left( {n,m} \right)} + {s\begin{pmatrix}{{{n\; \cos \; \theta} + {m\; \sin \; \theta}},} \\{{{- n}\; \sin \; \theta} + {m\; \cos \; \theta}}\end{pmatrix}}} \right\rbrack^{2}}}}} & (9)\end{matrix}$

The optimal result is similar conceptually to the decentration case.

$\begin{matrix}{s = {{- \frac{1}{\sum\limits_{\theta}{w(\theta)}}}\left\{ {\sum\limits_{\theta}{{w(\theta)}{p\left( {{{n\; \cos \; \theta} - {m\; \sin \; \theta}},{{n\; \sin \; \theta} + {m\; \cos \; \theta}}} \right)}}} \right\}}} & (10)\end{matrix}$

In a specific embodiment of the subject invention, the desired finalprogrammed size can be determined and the information describing the eyeaberration can be projected into a larger “transition” radius. FIG. 9shows an example of the pupil region and the transition region.Preferably, the extrapolation is continuous while decaying toward zero.Alternatively, these can be achieved after the optimization.

Optimizing with respect to rotation and decentration can be performedindependently. They may be done in either order depending on theexpectation of the physical behavior, yielding results that may not beexactly the same depending on the rotational symmetry of thedecentration range.

In an embodiment, the transition region may be deemphasized by applyinga decaying apodization. Further, the entire image may be refit withZernike polynomials.

T All patents, patent applications, provisional applications, andpublications referred to or cited herein are incorporated by referencein their entirety, including all figures and tables, to the extent theyare not inconsistent with the explicit teachings of this specification.

It should be understood that the examples and embodiments describedherein are for illustrative purposes only and that various modificationsor changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication.

1. A method for wavefront optimization process comprises, measuring rawwavefront data, considering frame fitting data selected from groupcomprising pupilary distance, vertex distance, pantascopic tilt, SEGheight, considering patient specific data such as desired usageconditions, considering spectacle geometry such as its length and widthincluding location of the pupil in the frame, and creating lensmanufacturing instructions that is based on determining optimumwavefront prescription, wherein the optimum wavefront prescriptioncomprises wavefront fitting and processing.
 2. The method of claim 1,wherein the lens manufacturing instructions may include a surface mapfor front and/or back side of a lens, a points file for freeform lensgenerator for custom front and back surfaces, a refractive index profilethat is created in a changeable refractive index layer, a refractiveindex profile that is created by ink-jet deposition, a stereolithographyprofile in conjunction with casting, or combination of any of the saidtechniques can be combined to achieve the custom lens manufacturing. 3.The method of claim 1, wherein the lens manufacturing instructions isapplied to a lens where the wavefront is emphasized along the centraloptical axis and de-emphasized outside the central optical axis toproduce aberration corrected single vision or progressive addition lens.4. The method of claim 1, wherein the wavefront fitting and processingcomprises method of determining lens wavefront.
 5. The method of claim4, wherein the method of determining lens wavefront comprises, measuringa patient's wavefront to create a pupil aberration, generating aplurality of corrected wavefronts, generating a function of theplurality of corrected wavefronts, determining a lens wavefront byoptimizing the function of the plurality of corrected wavefronts, andproducing a lens taking into account the lens wavefront.
 6. A method fordetermining a wavefront for a lens from a patient's measured wavefrontcomprises, measuring patient's wavefront aberrations, optimizing thecombined patient and lens wavefront aberrations, considering framefitting data selected from group comprising pupilary distance, vertexdistance, pantascopic tilt, SEG height, and use conditions, andproducing a spectacle lens with optimal correction across the entirelens.
 7. The method of claim 6, wherein the spectacle lens is producedby one of the methods that include a surface map for front and/or backside of a lens, a points file for freeform lens generator for customfront and back surfaces, a refractive index profile that is created in achangeable refractive index layer, a refractive index profile that iscreated by ink jet deposition, a stereolithography profile inconjunction with casting, or combination of any of the said techniquescan be combined to achieve the custom lens manufacturing.
 8. The methodof claim 6, wherein the spectacle lens produced is a single vision orprogressive addition lens and comprises wavefront that is emphasizedalong the central optical axis and de-emphasized outside the centraloptical axis.
 9. A method for determining lens wavefront comprises,optimizing a corrected wavefront, wherein the optimization involvesrepresenting the measured wavefront and the lens wavefront on a grid,wherein the grid lies in a plane, a subset of grid is used for therepresentation of the measured wavefront at a point on the grid so as totake into account the portions of the measured wavefront that contributeto the corrected wavefront at that point on the grid.
 10. The method ofclaim 9, wherein the corrected wavefront is the combined effect ofpatient's measured wavefront and the lens wavefront.
 11. The method ofclaim 9, wherein the optimization involves hill climbing optimizationtechnique such as Gaussian Least Squares Fit and Point SpreadOptimization software to fit an optimal wavefront across a specifiedsurface larger than that of the measured wavefront.
 12. The method ofclaim 11, wherein the optimal wavefront across a larger specifiedsurface involves projection from a number of points emanating inmultiple directions from a nominal axis of rotation representing thecenter of the eye.
 13. The method of claim 12, wherein the wavefront asprojected from the center of the eye can be convolved with a weightingfunction across the lens to enhance or emphasize the wavefront incertain area while allowing other areas to be de-emphasized.
 14. Themethod of claim 13, wherein the wavefront is best fit along a surfacerepresenting a paraxial lens representing the neutral axis of a lens,wherein the paraxial lens is fixed in space at a specified vertexdistance and follows the basic lens design curvature of the chosen lensblank.
 15. The method of claim 13, wherein the emphasized wavefront isin the central region of the lens where the distortion is reduced andthe de-emphasized area is when the patient is looking off center outsidethe central region.
 16. The method of claim 9, wherein the wavefrontpattern is solely based upon the low order aberrations, the high orderaberrations or combination of both low and high order aberrations.